Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions

HI!!

is it a hard equation ?

\[\sqrt{x+6}-4=x\]

oh no that can't be that hard

now you want to do it the math teacher way , or you want to think what the answer is , or both?

I'm not sure I understand what you're asking.

Okay

i can show you how to get the answer in your head second

Alright thanks :)

you want to get rid of the radical, so square both sides (carefully)

How would I square (x+4). Like this? x^2+8

\[\sqrt{x+6}=x+4\] square and get \[x+6=(x+4)^2\] or
\[x+6=(x+4)(x+4)\] or \[x+6=x^2+8x+16\]

Where did the 8x come from?

it is that old "first outer inner last" stuff

Ohhhh, FOIL okay..that makes sense.

so now we have
\[x+6=x^2+8x+16\] which is a quadratic equation we have to solve

set it equal to zero, get \[x^2+7x+10=0\] then factor

\[x^2+7x+10=0\\
(x+2)(x+5)=0\] so
\[x=-2,x=-5\] but we are not done yet

Making it an extraneous solution correct?

right , which is a silly way of saying it is not a solution but no matter

:) thank you @misty1212

\[\color\magenta\heartsuit\]